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with base angles of 72° and apex angle 36°. Two smaller copies of the same triangle may be drawn inside the given triangle, having the base of the triangle as one of their sides. The two new edges of these two smaller triangles, together with the base of the original golden triangle, form three of
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Some sources add another pentagram, inscribed within the inner pentagon of the largest pentagram of the figure. The other pentagons of the figure do not have inscribed pentagrams.
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the five edges of the polygon. Adding a segment between the endpoints of these two new edges cuts off a smaller golden triangle, within which the construction can be repeated.
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with three 108° angles and one 36° angle. The sizes of any two consecutive pentagrams in the sequence are in the
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Ellison, Elaine
Krajenke (2008), "Create a Mathematical Banner Using the Lute, the Sacred Cut, and the Spidron",
54:. The centers of the pentagrams lie on a line and (except for the first and largest of them) each shares two
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A Passion for
Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality
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to each other, and many other instances of the golden ratio appear within the lute.
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The
Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes
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Bridges
Leeuwarden: Mathematics, Music, Art, Architecture, Culture
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The lute is named after the ancient Greek mathematician
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61:An alternative construction is based on the
291:The Golden Relationship: Universal patterns
268:, John Wiley & Sons, pp. 331–332,
143:, W. W. Norton & Company, p. 420,
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58:with the next larger one in the sequence.
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50:The lute may be drawn from a sequence of
289:Boles, Martha; Newman, Rochelle (1990),
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175:, John Wiley & Sons, p. 260,
140:Mathematics: From the Birth of Numbers
293:, Pythagorean Press, pp. 86–87,
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205:"Strumming the Lute of Pythagoras"
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203:Lamb, Evelyn (May 29, 2013),
16:Self-similar geometric figure
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38:made from a sequence of
169:Darling, David (2004),
137:Gullberg, Jan (1997),
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260:Pickover, Clifford A.
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235:, pp. 467–468,
210:Scientific American
67:isosceles triangle
29:lute of Pythagoras
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23:Lute of Pythagoras
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33:self-similar
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83:convex hull
315:Categories
121:References
103:Pythagoras
87:kite shape
77:Properties
52:pentagrams
40:pentagrams
321:Fractals
262:(2011),
109:See also
56:vertices
115:Spidron
97:History
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65:, an
31:is a
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270:ISBN
237:ISBN
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
